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<p><dfn class="terminology">Theorem</dfn> If <span class="process-math">\(P_1(x), P_2(x),\cdots, P_n(x), g(x)\)</span> are continuous on an open interval <span class="process-math">\(I\text{,}\)</span> then the initial value problem (<a href="" class="xref" data-knowl="./knowl/eq4_1_1.html" title="Equation 4.1.2">(4.1.2)</a>) and (<a href="" class="xref" data-knowl="./knowl/eq4_2.html" title="Equation 4.1.3">(4.1.3)</a>) has a unique solution which is valid in <span class="process-math">\(I\text{.}\)</span></p>
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